# Count single node isolated sub-graphs in a disconnected graph

A disconnected Graph with N vertices and K edges is given. The task is to find the count of singleton sub-graphs. A singleton graph is one with only single vertex.**Examples:**

Input :Vertices : 6 Edges : 1 2 1 3 5 6Output :1Explanation :The Graph has 3 components : {1-2-3}, {5-6}, {4} Out of these, the only component forming singleton graph is {4}.

The idea is simple for graph given as adjacency list representation. We traverse the list and find the indices(representing a node) with no elements in list, i.e. no connected components.

Below is the representation :

## C++

`// CPP code to count the singleton sub-graphs` `// in a disconnected graph` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to compute the count` `int` `compute(vector<` `int` `> graph[], ` `int` `N)` `{` ` ` `// Storing intermediate result` ` ` `int` `count = 0;` ` ` `// Traversing the Nodes` ` ` `for` `(` `int` `i = 1; i <= N; i++)` ` ` `// Singleton component` ` ` `if` `(graph[i].size() == 0)` ` ` `count++; ` ` ` `// Returning the result` ` ` `return` `count;` `}` `// Driver` `int` `main()` `{` ` ` `// Number of nodes` ` ` `int` `N = 6;` ` ` `// Adjacency list for edges 1..6` ` ` `vector<` `int` `> graph[7];` ` ` `// Representing edges` ` ` `graph[1].push_back(2);` ` ` `graph[2].push_back(1);` ` ` `graph[2].push_back(3);` ` ` `graph[3].push_back(2);` ` ` `graph[5].push_back(6);` ` ` `graph[6].push_back(5);` ` ` `cout << compute(graph, N);` `}` |

## Java

`// Java code to count the singleton sub-graphs` `// in a disconnected graph` `import` `java.util.*;` `class` `GFG` `{` `// Function to compute the count` `static` `int` `compute(` `int` `[]graph, ` `int` `N)` `{` ` ` `// Storing intermediate result` ` ` `int` `count = ` `0` `;` ` ` ` ` `// Traversing the Nodes` ` ` `for` `(` `int` `i = ` `1` `; i < ` `7` `; i++)` ` ` `{` ` ` `// Singleton component` ` ` `if` `(graph[i] == ` `0` `)` ` ` `count++; ` ` ` `}` ` ` ` ` `// Returning the result` ` ` `return` `count;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `// Number of nodes` ` ` `int` `N = ` `6` `;` ` ` `// Adjacency list for edges 1..6` ` ` `int` `[]graph = ` `new` `int` `[` `7` `];` ` ` `// Representing edges` ` ` `graph[` `1` `] = ` `2` `;` ` ` `graph[` `2` `] = ` `1` `;` ` ` `graph[` `2` `] = ` `3` `;` ` ` `graph[` `3` `] = ` `2` `;` ` ` `graph[` `5` `] = ` `6` `;` ` ` `graph[` `6` `] = ` `5` `;` ` ` `System.out.println(compute(graph, N));` `}` `}` `// This code is contributed by PrinciRaj1992` |

## Python3

`# Python code to count the singleton sub-graphs` `# in a disconnected graph` ` ` `# Function to compute the count` `def` `compute(graph, N):` ` ` `# Storing intermediate result` ` ` `count ` `=` `0` ` ` ` ` `# Traversing the Nodes` ` ` `for` `i ` `in` `range` `(` `1` `, N` `+` `1` `):` ` ` ` ` `# Singleton component` ` ` `if` `(` `len` `(graph[i]) ` `=` `=` `0` `):` ` ` `count ` `+` `=` `1` ` ` ` ` `# Returning the result` ` ` `return` `count` ` ` `# Driver` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `# Number of nodes` ` ` `N ` `=` `6` ` ` ` ` `# Adjacency list for edges 1..6` ` ` `graph ` `=` `[[] ` `for` `i ` `in` `range` `(` `7` `)]` ` ` ` ` `# Representing edges` ` ` `graph[` `1` `].append(` `2` `)` ` ` `graph[` `2` `].append(` `1` `)` ` ` ` ` `graph[` `2` `].append(` `3` `)` ` ` `graph[` `3` `].append(` `2` `)` ` ` ` ` `graph[` `5` `].append(` `6` `)` ` ` `graph[` `6` `].append(` `5` `)` ` ` ` ` `print` `(compute(graph, N))` |

## C#

`// C# code to count the singleton sub-graphs` `// in a disconnected graph` `using` `System;` `class` `GFG` `{` `// Function to compute the count` `static` `int` `compute(` `int` `[]graph, ` `int` `N)` `{` ` ` `// Storing intermediate result` ` ` `int` `count = 0;` ` ` ` ` `// Traversing the Nodes` ` ` `for` `(` `int` `i = 1; i < 7; i++)` ` ` `{` ` ` `// Singleton component` ` ` `if` `(graph[i] == 0)` ` ` `count++; ` ` ` `}` ` ` ` ` `// Returning the result` ` ` `return` `count;` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` `// Number of nodes` ` ` `int` `N = 6;` ` ` `// Adjacency list for edges 1..6` ` ` `int` `[]graph = ` `new` `int` `[7];` ` ` ` ` `// Representing edges` ` ` `graph[1] = 2;` ` ` `graph[2] = 1;` ` ` `graph[2] = 3;` ` ` `graph[3] = 2;` ` ` `graph[5] = 6;` ` ` `graph[6] = 5;` ` ` `Console.WriteLine(compute(graph, N));` `}` `}` `// This code is contributed by 29AjayKumar` |

## Javascript

`<script>` `// JavaScript code to count the singleton sub-graphs` `// in a disconnected graph` `// Function to compute the count` `function` `compute(graph,N)` `{` ` ` `// Storing intermediate result` ` ` `let count = 0;` ` ` ` ` `// Traversing the Nodes` ` ` `for` `(let i = 1; i < 7; i++)` ` ` `{` ` ` `// Singleton component` ` ` `if` `(graph[i].length == 0)` ` ` `count++; ` ` ` `}` ` ` ` ` `// Returning the result` ` ` `return` `count;` `}` `// Driver Code` `// Number of nodes` `let N = 6;` `// Adjacency list for edges 1..6` `let graph = ` `new` `Array(7);` `for` `(let i=0;i<7;i++)` `{` ` ` `graph[i]=[];` `}` `// Representing edges` `graph[1].push(2)` `graph[2].push(1)` `graph[2].push(3)` `graph[3].push(2)` `graph[5].push(6)` `graph[6].push(5)` `document.write(compute(graph, N));` `// This code is contributed by rag2127` `</script>` |

**Output:**

1

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